The invention relates to an apparatus for three-dimensionally displaying an image by using voxel data obtained on a three-dimensional space and, more particularly, to a 3-dimensional image processing method which is effective in a 3-dimensional displaying apparatus using 3-dimensional data from a plurality of cross-sectional images scanned by a medical diagnosing apparatus (MRI, X-ray CT) for obtaining cross-sectional images.
The following prior art references 1) to 6) are well-known techniques related to the present invention.
1) "Nikkei Computer Graphics", December, 1988, pages 152 to 163.
2) "IEEE Trans. on Medical Imaging", Vol. 8, No. 3, pages 217 to 226, 1989.
3) "Radiology", April, 1989, pages 277 to 280.
4) "IEEE. Trans. on Medical Imaging", Vol. 9, No. 2, pages 178 to 183, 1990.
5) Azriel Rosenfeld, "Digital Picture Processing", translated by Makoto Nagao, pages 334 to 335.
6) JP-A-3-140140.
Three-dimensional image data (hereinafter, also referred to as 3-dimensional image data or 3D image data) is expressed by a set of small cubes called voxels. In the case of a two-dimensional (2-dimensional or 2D) image data, by directly displaying such 2D image data on a CRT, the 2D image can be seen by the human eyes. On the other hand, in the case of a 3D image, it is necessary to project the 3D image to 2D data in some format and to convert it into a form such that it can be viewed three-dimensionally. Such a process requires a perspective projection to convert a 3D image data into a 2D image, a hidden surface to eliminate the hidden portions which cannot be seen, and a shading to shade an image in order to obtain a stereoscopic feeling. Such a technique has been developed in the computer graphics (CG) field. In the medical 3-dimensional displaying process, the CG technique is conventionally used in the beginning. However, the conventional CG technique is not suitable for displaying a natural substance such as a human body. Such a CG technique has been developed as a method called a volume rendering.
The volume rendering methods are discussed in detail in the prior art reference 1) and 2).
It is an outline of those volume rendering methods that a boundary surface of an object to be displayed is not extracted but, on the basis of values in respective voxels, when the voxels are detected as a micro surface (voxel surface) on a 3-dimensional space, the light reflected by each voxel is obtained from the inclination of the surface and the light transmitted in the preceding voxel, and a 3D image is displayed as a sum of the reflected lights.
The example of the above method will now be practically explained with reference to FIG. 4.
It is now assumed that the ith voxel 401 on a projection line is set to V.sub.i, a voxel value 402 normalized to values from 0 to 1 for V.sub.i is set to f.sub.i, and an incident light 403 to the voxel V.sub.i is set to L.sub.i. When the incident light to the voxel V.sub.i passes in the voxel, it is reflected in accordance with the voxel value f.sub.i and is attenuated. The relation between the incident light L.sub.i to the voxel V.sub.i and a transmitted light L.sub.i+1 is expressed by the following equation. EQU L.sub.i+1 =L.sub.i (1-k(f.sub.i)) (1)
where, k is a function showing an attenuation factor of the voxel.
Picture quality changes in dependence on the setting of such a function. It is now assumed that the attenuation ratio of the voxel is proportional to the voxel value as a simple model. A region whose value is equal to or larger than a predetermined value .beta. is considered to be a complete boundary, so that no light is transmitted. On the other hand, since the light is attenuated by noises existing in front of the portion which is three-dimensionally displayed, a noise cut level .alpha. is set in order to avoid such a problem. The above points are summarized by the following equations. ##EQU1##
As will be obviously understood from the equation (1), the value of incident light L.sub.i is large on the surface of the object and is attenuated as the light progresses into the object. The value .SIGMA.{L.sub.i .multidot.f.sub.i } in which the products L.sub.i .multidot.f.sub.i of the incident light and the voxel values are accumulated with respect to all of the voxels on the projection line is the projection data to which the voxels of the object surface are reflected. The shading is performed by applying a weight to the product term L.sub.i .multidot.f.sub.i in the above equation in accordance with an angle which is defined by the incident light and the voxel surface. The voxel surface denotes a surface in which the voxels are regarded as one micro plane. A calculating method for the inclination of the voxel surface which is generally used is a method called gray-level gradients. In the above method, the gradients among the values of the adjacent voxels in three directions on a 3-dimensional space are used as a spatial gradient of the voxels. A vector gray-level gradient normalized to values from -1 to 1 is expressed by the following equation. EQU N.sub.i =.gradient.f.sub.i /.vertline..gradient.f.sub.i .vertline.(3)
where, ##EQU2##
The case where the light enters from the same direction as the projection line direction will now be considered. In such a case, since it is sufficient to consider only the z direction, N.sub.i is simply expressed by the following equation. ##EQU3##
From the above equation, a luminance g(x, y) on a projecting surface 404 is expressed by the following equation. EQU g(x, y)=.SIGMA.{f.sub.i .multidot.f.sub.i .multidot.cos .theta..sub.i }(5)
On the other hand, a method for calculating only one voxel on the surface extracted is called a surface rendering.
In any of the above rendering methods, in order to three-dimensionally display a designated organ existing inside of the body surface, it is necessary to extract the organ from the 3D voxel data. A method of automatically extracting the organ, however, has not yet established. To derive the accurate data, it does not help to use a method for manually inputting the outline of the organ every slice image. Since the required amount of three-dimensional data is extremely large, such an extraction of the organ by an operator is not practical in the clinical field where a real-time execution is required.
As region extracting methods which have been proposed to solve the above problem, the following two typical methods are known.
1 Method of extracting the outline of the designated region
2 Method of extracting region including the voxels in the designates region
The method of 1 is discussed in, for example, the prior art references 3) and 4) and is a method of extracting the outline of an organ by referring to a local value difference of the image. Hitherto, such a method has frequently been used for a medical image process.
The method 2 is discussed in the prior art reference.
5). One point in a region is first selected, points connected to the above point are sequentially searched from the adjacent voxels, and the region is expanded so as to include those connected points, thereby extracting the interest region. Such a method is generally called a Region Growing. A global gray-level condition such as a value difference between the average value of the whole region and each candidate point is ordinarily used as a condition (hereinafter, referred to as an expanding condition) to decide the connecting property. In the prior art reference 6), in addition to the global gray-level condition, boundary information such as a local gray-level change is combined and the region growing is executed in the 3-dimensional space instead of the 2-dimensional space, thereby realizing the region extraction of a higher reliability.
In the prior art references 1) and 2), on the other hand, the editing (addition, correction, erasure, etc.) of a 3D image is discussed. In the prior art reference 1), there is described a method whereby a matrix called a mat volume in which values correspond to voxels in a one-to-one corresponding relation is used and the values are stored into a portion to be cut out and the editing is performed by the matrix calculation. In the prior art reference 2), an interactive 3-dimensional image processing system (ANALYZE) using the volume rendering method is described in detail. In the above system, a function to cut a 3-dimensional portion is also mentioned as a function to edit a 3D image.
In the above conventional techniques, any of the extracting methods of the prior art references 3) to 6) depends on the characteristics of the voxel data as an object, so that it is difficult to completely extract an interest region. In order to always obtain a clinically adequate image, the interposition of an operator is inevitable in the procedure of extraction. However, nothing is considered with respect to a point of interactive edition of image data during the extraction. On the other hand, although the edition of a 3D image is discussed in the prior art references 1) and 2), such an editing relates to an editing function for the final result and nothing is described with respect to a method where the processing procedure such as a region extraction or the like is three-dimensionally perspectively projected and displayed. In any of the above methods, consequently, the extracting process for a 3D image as an object cannot be efficiently performed.